Mathematical Investigations IV
S&S Unit test
Name ______________
You may use a TI-30 Calculator on this exam. Justify all your work.
1.
(2 pts each) Given the numbers 8 and 128, find their:
a) arithmetic mean
2.
b) geometric mean
Consider the series 4  7  5  8  6  9 
a. (4 pts) Write the series in
 62  65 .
  notation.
b. (5 pts) Use appropriate formulas to evaluate the series.
c) harmonic mean
Mathematical Investigations IV
3.
S&S Unit test
(3 pts each) If a series has a first term of 16 and the sum of its first three terms is 76, find:
a. The common ratio if the series is geometric.
b. The common difference if the series is arithmetic.
4.
Name ______________
(3 pts each) Write out the first four terms of:
a. The sequence rn  n1 if
if n  1
 5

rn   3
if n  2
r  2r if n  2
n2
 n 1
92
b. The series
 (2
k 1
k
 4k )
Mathematical Investigations IV
5.
S&S Unit test
Name ______________
n
(4 pts) Let S n   ak . Suppose that Sn  n 2  7n  1 for all positive integers n.
k 1
Determine the first three terms of the sequence ak k 1 .

6.
(3 pts each) Write:
a. A recursive formula for the sequence defined by bn 
18
.
3n
if n  1
 7
b. An explicit formula for the sequence defined by: cn  
cn1  2 if n  1
Mathematical Investigations IV
S&S Unit test
Name ______________
n
7.
Let S n represent the nth partial sum of the series
 4k
k 1
8
2
1
.
a. (4 pts) Use mathematical induction to prove that S n  4 
4
for all positive integers n.
2n  1

b. (2 pts) Use the formula in part a. to determine the value of
 4k
k 1
8
2
1